Lower bound on the magnetic field strength in the hot universe

TL;DR

This paper estimates a lower bound on primordial magnetic field strength in the early universe, suggesting it was at least 10^{14} G during the electroweak phase transition, based on vacuum polarization effects.

Contribution

It develops a method to estimate magnetic field strengths at different temperatures and derives a lower bound at the electroweak transition, considering the standard model.

Findings

Lower bound on magnetic field strength at electroweak transition: ~10^{14} G

Vacuum polarization of non-Abelian gauge fields can generate primordial magnetic fields

Zero screening mass indicates long-range coherence of early universe magnetic fields

Abstract

It is assumed that long range coherent magnetic fields in the universe were spontaneously generated at high temperature due to vacuum polarization of non-Abelian gauge fields, and resulted in the present intergalaxy magnetic field. The zero value of the screening mass for fields of this type was discovered recently. Here, a procedure to estimate the field strengths at different temperatures is developed and the lower bound on the magnetic field strength $B \sim 10^{14} G$, at the electroweak phase transition temperature, is derived. As a particular case, the standard model is considered. Some model dependent peculiarities of the phenomena under investigation are briefly discussed.